A trapezoidal channel with a bottom width $5m,$ free surface width $10m$ and depth $2\mathrm{.}2m$ is shown in

Figure $2.$ The discharge is stabilized at $120\frac{m^3}{s}.$ The surface of the channel are lined with asphalt and

Manning's $n=0\mathrm{.}016.$

$($i$)$ Calculate the hydraulic radius.

$($ii$)$ Determine the free surfaro